Standards and Objectives

AGP.1.2: add, subtract, multiply, and divide decimals, integers, fractions and mixed numbers.

Fractions with Unlike Denominators

AGP.1.3: use order relations to compare, order, or locate whole numbers, integers, fractions, and decimals on a number line.

Comparing and Ordering Decimals

Comparing and Ordering Fractions

Comparing and Ordering Rational Numbers

AGP.2.2: solve equations with at least two operations.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

AGP.3.1: use a compass to construct congruent angles, bisect angles, and bisect line segments.

Constructing Congruent Segments and Angles

AGP.3.2: estimate and find circumference and area of a circle.

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

AGP.3.3: estimate and find the area and perimeter of polygons

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

AGP.3.4: estimate and find the surface area and the volume of three-dimensional figures.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

AGP.3.5: identify angle relationships: complementary, supplementary, vertical, and adjacent.

Investigating Angle Theorems - Activity A

AGP.3.6: identify angle relationships; involving parallel lines and apply in solving problems (corresponding angles, alternate interior angles, and alternate exterior angles).

Investigating Angle Theorems - Activity A

AGP.3.7: investigate similar triangles and apply proportions in problem solving situations.

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

AGP.3.8: develop and explore circle relationships, emphasizing the vocabulary of circles.

AGP.4.2: use a protractor to measure and draw angles.

Constructing Congruent Segments and Angles

AGP.5.1: read, interpret, and construct graphs to solve problems.

Box-and-Whisker Plots

Histograms

Line Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

AGP.5.2: use data to determine mean, median, mode, and range.

Box-and-Whisker Plots

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

A1.2.1: simplify and evaluate algebraic expressions using grouping symbols, order of operations and properties of real numbers with justification of steps.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Radicals - Activity A

A1.2.2: solve multi-step linear equations in one variable and apply skills toward solving practical problems.

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

A1.2.4: solve literal equations for a given variable and apply the skills toward solving practical problems.

Solving Formulas for any Variable

A1.2.5: analyze a given set of data for the existence of a pattern numerically, algebraically and graphically; determine the domain and range; and determine if the relation is a function.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Introduction to Functions

A1.2.7: use the laws of exponents to perform operations on expressions with integral exponents.

Dividing Exponential Expressions

Exponential Functions - Activity A

Exponents and Power Rules

Multiplying Exponential Expressions

A1.2.8: determine the slope of a line given an equation of a line, the graph of a line and two points to be identified.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

A1.2.9: graph linear equations using slope-intercept, point slope, and x- and y-intercepts.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

A1.2.10: write an equation of a line given a graph of a line, two points on the line, the slope and a point, and the slope and y-intercept.

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

A1.2.11: solve systems of linear equations numerically and graphically, by the elimination method and by the substitution method.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

A1.2.12: add and subtract polynomials.

Addition of Polynomials - Activity A

A1.2.13: multiply and divide binomials by binomials or monomials.

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

A1.2.14: factor polynomials by using appropriate methods.

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

A1.2.15: estimate and simplify square roots into both exact and approximate forms.

Simplifying Radicals - Activity A

Square Roots

A1.2.16: solve quadratic equations by graphing, factoring and quadratic formula.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

A1.2.18: collect, organize, interpret data and predict outcomes using the mean, mode, median, and range.

Describing Data Using Statistics

Mean, Median and Mode

A1.2.20: predict the outcomes of simple events using the rules of probability.

Geometric Probability - Activity A

A1.2.21: use process (flow) charts and histograms, scatter diagrams and normal distribution curves.

Histograms

Populations and Samples

Scatter Plots - Activity A

Solving Using Trend Lines

AM1.2.1: solve practical problems involving computation using estimation.

AM1.2.3: distinguish between counting and measuring using micrometers, calipers and other precision tools to make measurements.

AM1.2.4: solve practical problems and interpret results using rational numbers and vectors.

Fractions with Unlike Denominators

Vectors

AM1.2.6: translate word phrases into algebraic expressions or word sentences into equations and inequalities.

Using Algebraic Equations

Using Algebraic Expressions

AM1.2.8: solve literal equations for a given variable and apply the skills toward solving practical problems.

Solving Formulas for any Variable

AM1.2.10: solve multi-step linear equations in one variable and apply skills toward solving practical problems.

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

AM1.2.11: solve multi-step linear inequalities in one variable, interpret the results on a number line and apply the skills toward solving practical problems.

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

AM1.2.13: collect, organize, interpret data, and predict outcomes using the mean, mode, median, range and standard deviation.

Describing Data Using Statistics

Mean, Median and Mode

AM1.2.14: estimate and simplify square roots into both exact and approximate forms.

Simplifying Radicals - Activity A

Square Roots

AM1.2.15: use the laws of exponents to perform operations on expressions with integral exponents.

Dividing Exponential Expressions

Exponential Functions - Activity A

Exponents and Power Rules

Multiplying Exponential Expressions

AM1.2.16: predict the outcomes of simple events using the rules of probability.

Geometric Probability - Activity A

AM2.2.1: analyze a given set of data for the existence of a pattern numerically, algebraically and graphically; determine the domain and range; and determine if the relation is a function.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Introduction to Functions

AM2.2.2: determine the slope of a line given an equation of a line, the graph of a line and two points to be identified.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

AM2.2.3: graph linear equations using slope-intercept, point slope, and x- and y-intercepts.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

AM2.2.4: write an equation of a line given graph of a line, two points on the line, the slope and a point, and the slope and y-intercept.

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

AM2.2.5: solve systems of linear equations numerically and graphically, by the elimination method and by the substitution method.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

AM2.2.6: add and subtract polynomials.

Addition of Polynomials - Activity A

AM2.2.7: multiply and divide binomials by binomials or monomials.

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

AM2.2.8: factor polynomials by using appropriate methods.

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

AM2.2.9: solve quadratic equations by graphing, factoring and quadratic formula.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

AM2.2.11: use process (flow) charts and histograms, scatter diagrams, and normal distribution curves in order to perform statistical process (quality) control.

Histograms

Populations and Samples

Scatter Plots - Activity A

Solving Using Trend Lines

G.3.2: differentiate between inductive and deductive reasoning.

Biconditional Statement

Conditional Statement

G.3.4: construct logical arguments in formal and informal methods with direct and indirect reasoning.

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.3.5: apply definitions, theorems, and postulates related to such topics as complementary, supplementary, and vertical angles and angles formed by perpendicular lines.

Investigating Angle Theorems - Activity A

G.3.6: explore the relationship between angles formed by two lines cut by a transversal when lines are and are not parallel, and use the results to develop methods to show parallelism.

Investigating Angle Theorems - Activity A

G.3.7: investigate and verify congruence relationships in triangles.

Congruence in Right Triangles

Proving Triangles Congruent

G.3.8: explore and identify properties of quadrilaterals and verify the properties for parallelograms, rectangles, rhombuses, squares, and trapezoids.

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

G.3.9: investigate measures of angles and lengths of segments to determine the existence of triangles (triangle inequality) and the order of sides and unknown side lengths or angles and inaccessible heights and distances, construct scaled drawings, and derive the basis for the trigonometric ratios.

Simplifying Trigonometric Expressions

Triangle Inequalities

G.3.10: using trigonometric ratios, determine lengths of sides and measures of angles in right triangles.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.3.11: apply the Pythagorean Theorem and its converse in solving practical problems and in deriving the special right triangle relationships.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

G.3.12: investigate measures of angles formed by chords, tangents, and secants of a circle and the relationship to its arcs.

G.3.13: given a polygon, find angle measures of interior and exterior angles; find length of sides from given data; and use properties of regular polygons to find missing data.

Classifying Triangles

Triangle Angle Sum - Activity A

G.3.15: develop and apply formulas for area, perimeter, surface area, and volume and apply them in the modeling of practical problems.

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Rectangle: Perimeter and Area

G.3.16: develop and apply concepts of analytical geometry such as formulas for distance, slope, and midpoint and apply these to finding dimensions of polygons on the coordinate plane.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Slope - Activity B

G.3.17: using various methods, construct a triangleâ€™s medians, altitudes, angle and perpendicular bisectors; identify conjectures and develop mathematical arguments about their relationships.

Concurrent Lines, Medians, and Altitudes

G.3.18: using transformational geometry, create a reflection, translation, rotation, glide reflection and dilation of a figure; and apply transformations and use symmetry to analyze mathematical situations.

Dilations

Holiday Snowflake Designer

Reflections

Rotations, Reflections and Translations

Translations

A2.2.1: write equations of lines given various information including parallel and perpendicular lines and vertical and horizontal lines.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Standard Form of a Line

A2.2.5: simplify radicals and expressions involving fractional exponents and convert between the two forms.

Operations with Radical Expressions

Simplifying Radicals - Activity A

A2.2.6: solve quadratic equations over the set of complex numbers: apply the techniques of factoring and completing the square and the quadratic formula; use the discriminate to determine the nature of the roots; confirm the solutions numerically and graphically; and apply to practical problems.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

A2.2.9: define a function: find the domain, range, zeros; find the inverse of a function; find the value of a function for a given element in its domain; and perform basic operations on functions including composition of functions.

Introduction to Functions

Polynomials and Linear Factors

A2.2.10: explore basic families of functions: recognize linear, quadratic, absolute value, step, and exponential functions; and convert among graphs, tables and equations.

Exponential Functions - Activity A

Inequalities Involving Absolute Values

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A2.2.11: solve quadratic inequalities and graph their solution sets.

Linear Inequalities in Two Variables - Activity A

Quadratic Inequalities - Activity A

A2.2.12: solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum and minimum values of a function over a region using linear program techniques

Linear Functions

Linear Programming - Activity A

A2.2.13: solve practical problems involving direct, inverse, and joint variation.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

A2.2.14: explore the conic sections; recognize, identify, and sketch the graphs of a parabola, circle, ellipse, and hyperbola; and convert between graphs and equations.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Quadratics in Factored Form

A2.2.15: solve absolute value equations and inequalities graphically, numerically, and algebraically.

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

A2.2.16: define a logarithmic function: transform equations from exponential form into logarithmic form; and apply the basic properties of logarithms to simplify or expand an expression.

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

CM.2.1: develop a variety of problem solving strategies (e.g., draw a diagram, look for a pattern, and work backwards).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

CM.2.2: interpret graphs of functions (i.e., linear, quadratic, exponential).

Exponential Functions - Activity A

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

CM.2.3: solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.

Exponential Functions - Activity A

Linear Functions

CM.2.5: calculate costs, simple and compound interest, finance charges, loan payments and taxes.

CM.3.1: apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Perimeters and Areas of Similar Figures

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Similar Figures - Activity A

Similar Polygons

CM.3.2: solve workplace problems involving perimeter, area, surface area and volume.

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

CM.3.3: investigate the applications of various geometric shapes and patterns to art, architecture, and nature.

CM.5.2: integrate other disciplines into the study of mathematics through simulations, research, and projects

CM.5.3: determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

Binomial Probabilities

Permutations

Permutations and Combinations

CM.5.5: create and interpret data using various methods of displaying numerical data, including frequency distributions, graphs, histograms, stem-and-leaf plots, and box-and-whiskers plots, using technology when appropriate.

Box-and-Whisker Plots

Histograms

Populations and Samples

Stem-and-Leaf Plots

CM.5.6: relate the measures of central tendency and the measures of dispersion to a normal distribution.

Line Plots

Mean, Median and Mode

CM.5.7: apply the measures of central tendency and the measures of dispersion to workplace situations.

Line Plots

Mean, Median and Mode

T.3.1: define the six trigonometric functions in terms of a right triangle and find the values of the functions of an angle in standard position, given a point on the terminal side of the angle. Circular function definitions will be connected with trigonometric function definitions.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.3.2: find the values of the other trigonometric functions, given the value of one trigonometric function.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.3.3: develop recall of the values of the six trigonometric functions of special angles as related to the unit circle.

Cosine Function

Simplifying Trigonometric Expressions

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

T.3.4: use a calculator to find the values of the trigonometric functions for any angle and to find the measure of an angle given the value of one of its trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.3.5: convert angle measures from radians to degrees and vice versa.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.3.6: verify trigonometric identities by making substitutions and recalling basic identities.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

T.3.9: find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula).

Classifying Triangles

Perimeter, Circumference, and Area - Activity B

T.3.10: express complex numbers in polar form: perform operations including adding, subtracting, multiplying, and dividing; evaluate powers and roots of complex numbers using De Moivre's Theorem; and graph complex numbers.

T.3.11: solve practical problems involving triangles using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines.

Cosine Function

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Sine Function

Tangent Function

Unit Circle

T.3.12: recognize the graph of the six trigonometric functions. Given an equation in the form of y=aSin(bx+c)+d, identify the domain and range; determine the period, phase shift, amplitude and vertical shift; and sketch at least one period of the graph.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

T.3.13: model periodic data sets using graphs, tables, and equations.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

T.3.15: develop and use formulas such as sum or difference of two angles, double-angle, and halfangle.

Sum and Difference Identities for Sine and Cosine

T.3.16: perform mathematical operations with vectors and use vectors to solve practical problems.

PS.5.1: distinguish between experimental and theoretical probability.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Polling: City

Probability Simulations

Theoretical and Experimental Probability

PS.5.2: create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves, and make predictions about outliers.

PS.5.3: determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

Binomial Probabilities

Permutations

Permutations and Combinations

PS.5.4: express the chances of events occurring either in terms of a probability or odds.

Binomial Probabilities

Geometric Probability - Activity A

PS.5.5: use the normal distribution and the binomial distribution including pascal's triangle, to determine probability of events.

PS.5.6: interpret and calculate measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs or from data created through experimentation.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

PS.5.7: interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation.

Box-and-Whisker Plots

Describing Data Using Statistics

PS.5.9: describe the role of sampling, randomness, bias, and sample size in data collection and interpretation.

PS.5.12: determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable.

Correlation

Solving Using Trend Lines

PC.2.1: investigate and sketch the graphs of polynomials and rational functions using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points and domain and range.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

General Form of a Rational Function

Polynomials and Linear Factors

Rational Functions

PC.2.2: solve higher order polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, and Rational Root Theorem.

Dividing Polynomials Using Synthetic Division

PC.2.4: establish the relationship between exponential and logarithmic functions; graph related functions and include their domain and range.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Introduction to Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

PC.2.5: solve equations and practical problems involving exponential and logarithmic expressions: include natural and common logarithms; use laws of exponents; and confirm solutions graphically and numerically.

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

PC.2.7: find the limit of a function, a sequence, or a series by graphing, intuitive reasoning, algebraic methods, and numerical substitution.

Roots of a Quadratic

Translating and Scaling Functions

Using Algebraic Equations

PC.2.8: perform mathematical operations with vectors and use vectors to solve practical problems.

PC.3.1: graph functions and conic sections using translation.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Rotations, Reflections and Translations

Translations

PC.3.2: investigate properties and solve practical problems of the conic sections.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Correlation last revised: 12/4/2008